The notes of F6/9 are F, A, C, D and G. F is the root, A the major third, C the fifth, D the sixth and G the ninth.
String by string, low to high, it plays F, A, D, G, C and F. The root, F, shows up twice in the main shape. The lowest and highest notes are both F, two octaves apart, on strings 6 and 1.
The open strings add notes to F6/9 too. String 5 gives A, string 4 gives D and string 3 gives G. Every finger presses at fret 1. There is one more position, starting at fret 7.
Inside F6/9 sits a complete Dm chord, made of F, A and D. F shares three positions with this shape.
F6/9 shows up in six keys. In F major it is the I6/9, in Bb major the V6/9 and in C major the IV6/9. The rest appear in the key list.